Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

Partial duplication of the APBA2 gene in chromosome 15q13 corresponds to duplicon structures.

BackgroundChromosomal abnormalities affecting human chromosome 15q11-q13 underlie multiple genomic disorders caused by deletion, duplication and triplication of intervals in this region. These events are mediated by highly homologous segments of DNA, or duplicons, that facilitate mispairing and unequal cross-over in meiosis. The gene encoding an amyloid precursor protein-binding protein (APBA2) was previously mapped to the distal portion of the interval commonly deleted in Prader-Willi and Angelman syndromes and duplicated in cases of autism.ResultsWe show that this gene actually maps to a more telomeric location and is partially duplicated within the broader region. Two highly homologous copies of an interval containing a large 5' exon and downstream sequence are located approximately 5 Mb distal to the intact locus. The duplicated copies, containing the first coding exon of APBA2, can be distinguished by single nucleotide sequence differences and are transcriptionally inactive. Adjacent to APBA2 maps a gene termed KIAA0574. The protein encoded by this gene is weakly homologous to a protein termed X123 that in turn maps adjacent to APBA1 on 9q21.12; APBA1 is highly homologous to APBA2 in the C-terminal region and is distinguished from APBA2 by the N-terminal region encoded by this duplicated exon.ConclusionThe duplication of APBA2 sequences in this region adds to a complex picture of different low copy repeats present across this region and elsewhere on the chromosome

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

Exploratory study of the state of environmentally conscious design in the medical device industry

This exploratory study seeks to explore the current state of design for the environment (DfE) in the development of medical devices; an historically risk averse industry that lags behind others in terms of addressing environmental considerations. A cross-sectional survey of 34 medical device designers, primarily in the UK and USA, was conducted in order to fulfil this objective. Findings indicate that there is significant motivation to enhance DfE practice, but that there are multiple barriers to this. Major barriers identified are a perception of the high cost of DfE, the industry’s current reliance on a single-use business model for many current products and a lack of education about DfE topics on all sides. Designers felt that the most significant opportunities to implement DfE are in situations where they are able to exert direct control, mainly in the early stages of the design process. Issues noted include raw material choice and packaging decisions. The nature of single use business models is also critical, pointing towards the needs for a systemic rather than product focus. For this to be achieved, financial rewards must be evident to firms and the changing regulatory landscape might also make a more significant impact.This research was supported using funding from the Engineering and Physical Sciences Research Council (EPSRC) in the United Kingdom, grant number EP/E001769/1.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jclepro.2015.06.01

A maturity grid assessment tool for environmentally conscious design in the medical device industry

The medical device industry is growing increasingly concerned about environmental impact of products. Whilst there are many tools aiming to support environmentally conscious design, they are typically complex to use, demand substantial data collection and are not tailored to the specific needs of the medical device sector. This paper reports on the development of a Maturity Grid to address this gap. This novel design tool was developed iteratively through application in five case studies. The tool captures principles of eco-design for medical devices in a simple form, designed to be used by a team. This intervention tool provides designers and product marketers with insights on how to improve the design of their medical devices and specifically allows consideration of the complex trade-offs between decisions that influence different life-cycle stages. Through the tool, actionable insight is created that supports decisions to be made within the realm of design engineers and beyond. The tool highlights areas which are influenced by design decisions taken, some of which are perceived to be outside of the direct control of designers.This work was by the United Kingdom’s Engineering and Physical Sciences Research, [Grant Number EP/E001769/1]